Eleftherios Matsikoudis and Edward A. Lee

EECS Department, University of California, Berkeley

Technical Report No. UCB/EECS-2013-122

June 9, 2013

http://www2.eecs.berkeley.edu/Pubs/TechRpts/2013/EECS-2013-122.pdf

We ask whether strictly causal components form well defined systems when arranged in feedback configurations. The standard interpretation for such configurations induces a fixed-point constraint on the function modelling the component involved. We define strictly causal functions formally, and show that the corresponding fixed-point problem does not always have a well defined solution. We examine the relationship between these functions and the functions that are strictly contracting with respect to a generalized distance function on signals, and argue that these strictly contracting functions are actually the functions that one ought to be interested in. We prove a constructive fixed-point theorem for these functions, introduce a corresponding induction principle, and study the related convergence process.

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BibTeX citation:

@techreport{Matsikoudis:EECS-2013-122,
    Author= {Matsikoudis, Eleftherios and Lee, Edward A.},
    Title= {The Fixed-Point Theory of Strictly Causal Functions},
    Year= {2013},
    Month= {Jun},
    Url= {http://www2.eecs.berkeley.edu/Pubs/TechRpts/2013/EECS-2013-122.html},
    Number= {UCB/EECS-2013-122},
    Abstract= {We ask whether strictly causal components form well defined systems when arranged in feedback configurations. The standard interpretation for such configurations induces a fixed-point constraint on the function modelling the component involved. We define strictly causal functions formally, and show that the corresponding fixed-point problem does not always have a well defined solution. We examine the relationship between these functions and the functions that are strictly contracting with respect to a generalized distance function on signals, and argue that these strictly contracting functions are actually the functions that one ought to be interested in. We prove a constructive fixed-point theorem for these functions, introduce a corresponding induction principle, and study the related convergence process.},
}

EndNote citation:

%0 Report
%A Matsikoudis, Eleftherios 
%A Lee, Edward A. 
%T The Fixed-Point Theory of Strictly Causal Functions
%I EECS Department, University of California, Berkeley
%D 2013
%8 June 9
%@ UCB/EECS-2013-122
%U http://www2.eecs.berkeley.edu/Pubs/TechRpts/2013/EECS-2013-122.html
%F Matsikoudis:EECS-2013-122